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Open-source constraint solver.
/*
* This file is part of choco-solver, http://choco-solver.org/
*
* Copyright (c) 2022, IMT Atlantique. All rights reserved.
*
* Licensed under the BSD 4-clause license.
*
* See LICENSE file in the project root for full license information.
*/
package org.chocosolver.solver.constraints;
import org.chocosolver.solver.ISelf;
import org.chocosolver.solver.Model;
import org.chocosolver.solver.constraints.binary.PropGreaterOrEqualX_Y;
import org.chocosolver.solver.constraints.graph.basic.*;
import org.chocosolver.solver.constraints.graph.channeling.edges.*;
import org.chocosolver.solver.constraints.graph.channeling.nodes.PropNodeBoolChannel;
import org.chocosolver.solver.constraints.graph.channeling.nodes.PropNodeBoolsChannel;
import org.chocosolver.solver.constraints.graph.channeling.nodes.PropNodeSetChannel;
import org.chocosolver.solver.constraints.graph.connectivity.*;
import org.chocosolver.solver.constraints.graph.cost.trees.PropMaxDegVarTree;
import org.chocosolver.solver.constraints.graph.cost.trees.PropTreeCostSimple;
import org.chocosolver.solver.constraints.graph.cost.trees.lagrangian.PropGenericLagrDCMST;
import org.chocosolver.solver.constraints.graph.cost.tsp.PropCycleCostSimple;
import org.chocosolver.solver.constraints.graph.cost.tsp.lagrangian.PropLagrOneTree;
import org.chocosolver.solver.constraints.graph.cycles.PropAcyclic;
import org.chocosolver.solver.constraints.graph.cycles.PropCycle;
import org.chocosolver.solver.constraints.graph.degree.PropNodeDegreeAtLeastIncr;
import org.chocosolver.solver.constraints.graph.degree.PropNodeDegreeAtMostIncr;
import org.chocosolver.solver.constraints.graph.degree.PropNodeDegreeVar;
import org.chocosolver.solver.constraints.graph.inclusion.PropInclusion;
import org.chocosolver.solver.constraints.graph.symmbreaking.PropIncrementalAdjacencyMatrix;
import org.chocosolver.solver.constraints.graph.symmbreaking.PropIncrementalAdjacencyUndirectedMatrix;
import org.chocosolver.solver.constraints.graph.symmbreaking.PropSymmetryBreaking;
import org.chocosolver.solver.constraints.graph.symmbreaking.PropSymmetryBreakingEx;
import org.chocosolver.solver.constraints.graph.tree.PropArborescence;
import org.chocosolver.solver.constraints.graph.tree.PropArborescences;
import org.chocosolver.solver.constraints.graph.tree.PropReachability;
import org.chocosolver.solver.variables.*;
import org.chocosolver.util.objects.graphs.Orientation;
import org.chocosolver.util.tools.ArrayUtils;
/**
* Some usual graph constraints
*
* @author Jean-Guillaume Fages
*/
public interface IGraphConstraintFactory extends ISelf {
//***********************************************************************************
// BASIC CONSTRAINTS
//***********************************************************************************
// counting
/**
* Create a constraint to force the number of nodes in g to be equal to nb
*
* @param g a graph variable
* @param nb an integer variable indicating the expected number of nodes in g
* @return A constraint to force the number of nodes in g to be equal to nb
*/
default Constraint nbNodes(GraphVar g, IntVar nb) {
return new Constraint("nbNodes", new PropNbNodes(g, nb));
}
/**
* Create a constraint to force the number of edges in g to be equal to nb
*
* @param g a graph variable
* @param nb an integer variable indicating the expected number of edges in g
* @return A constraint to force the number of edges in g to be equal to nb
*/
default Constraint nbEdges(GraphVar g, IntVar nb) {
return new Constraint("nbEdges", new PropNbEdges(g, nb));
}
// loops
/**
* Create a constraint which ensures that 'loops' denotes the set
* of vertices in g which have a loop, i.e. an edge of the form f(i,i)
* i.e. vertex i in g => edge (i,i) in g
*
* @param g a graph variable
* @return A constraint which makes sure every node has a loop
*/
default Constraint loopSet(GraphVar g, SetVar loops) {
return new Constraint("loopSet", new PropLoopSet(g, loops));
}
/**
* Create a constraint which ensures g has nb loops
* |(i,i) in g| = nb
*
* @param g a graph variable
* @param nb an integer variable counting the number of loops in g
* @return A constraint which ensures g has nb loops
*/
default Constraint nbLoops(GraphVar g, IntVar nb) {
return new Constraint("nbLoops", new PropNbLoops(g, nb));
}
//***********************************************************************************
// SIMPLE PROPERTY CONSTRAINTS
//***********************************************************************************
// symmetry
/**
* Creates a constraint which ensures that g is a symmetric directed graph
* This means (i,j) in g <=> (j,i) in g
* Note that it may be preferable to use an undirected graph variable instead!
*
* @param g a directed graph variable
* @return A constraint which ensures that g is a symmetric directed graph
*/
default Constraint symmetric(DirectedGraphVar g) {
return new Constraint("symmetric", new PropSymmetric(g));
}
/**
* Creates a constraint which ensures that g is an antisymmetric directed graph
* This means (i,j) in g => (j,i) notin g
*
* @param g a directed graph variable
* @return A constraint which ensures that g is an antisymmetric directed graph
*/
default Constraint antisymmetric(DirectedGraphVar g) {
return new Constraint("antisymmetric", new PropAntiSymmetric(g));
}
// Transitivity
/**
* Create a transitivity constraint
* (i,j) in g and (j,k) in g => (i,k) in g
* Does not consider loops
* Enables to make cliques
*
* @param g A graph variable
* @return A transitivity constraint
*/
default Constraint transitivity(GraphVar g) {
return new Constraint("transitivity", new PropTransitivity(g));
}
//***********************************************************************************
// INCLUSION CONSTRAINTS
//***********************************************************************************
/**
* Create an inclusion constraint between g1 and g2 such that
* g1 is a subgraph of g2
* Note that node are labelled with their indexes :
* the vertex 0 in g1 corresponds to the vertex 0 in g2
*
* @param g1 An undirected graph variable
* @param g2 An undirected graph variable
* @return a constraint which ensures that g1 is a subgraph of g2
*/
default Constraint subgraph(UndirectedGraphVar g1, UndirectedGraphVar g2) {
return new Constraint("subgraph", new PropInclusion(g1, g2));
}
/**
* Create an inclusion constraint between g1 and g2 such that
* g1 is a subgraph of g2
* Note that node are labelled with their indexes :
* the vertex 0 in g1 corresponds to the vertex 0 in g2
*
* @param g1 A directed graph variable
* @param g2 A directed graph variable
* @return a constraint which ensures that g1 is a subGraph of g2
*/
default Constraint subgraph(DirectedGraphVar g1, DirectedGraphVar g2) {
return new Constraint("subgraph", new PropInclusion(g1, g2));
}
//***********************************************************************************
// CHANNELING CONSTRAINTS
//***********************************************************************************
// Vertices
/**
* Channeling constraint :
* int i in nodes <=> vertex i in g
*
* @param g
* @param nodes
*/
default Constraint nodesChanneling(GraphVar g, SetVar nodes) {
return new Constraint("nodesSetChanneling",
new PropNodeSetChannel(nodes, g));
}
/**
* Channeling constraint :
* nodes[i] = 1 <=> vertex i in g
*
* @param g
* @param nodes
*/
default Constraint nodesChanneling(GraphVar g, BoolVar[] nodes) {
return new Constraint("nodesBoolsChanneling",
new PropNodeBoolsChannel(nodes, g));
}
/**
* Channeling constraint :
* isIn = 1 <=> vertex 'vertex' in g
*
* @param g
* @param isIn
* @param vertex
*/
default Constraint nodeChanneling(GraphVar g, BoolVar isIn, int vertex) {
return new Constraint("nodesBoolChanneling",
new PropNodeBoolChannel(isIn, vertex, g));
}
// Directed edges
/**
* Channeling constraint :
* isEdge = 1 <=> edge (from,to) in g
*
* @param g
* @param isEdge
* @param from
* @param to
*/
default Constraint edgeChanneling(DirectedGraphVar g, BoolVar isEdge, int from, int to) {
return new Constraint("edgeChanneling",
new PropEdgeBoolChannel(isEdge, from, to, g));
}
// Edge
/**
* Channeling constraint:
* isEdge = 1 <=> edge (i,j) in g
*
* @param g
* @param isEdge
* @param i
* @param j
*/
default Constraint edgeChanneling(UndirectedGraphVar g, BoolVar isEdge, int i, int j) {
return new Constraint("edgeChanneling",
new PropEdgeBoolChannel(isEdge, i, j, g));
}
// Neighbors
/**
* Channeling constraint:
* int j in neighbors[i] <=> edge (i,j) in g
*
* @param g
* @param neighbors
*/
default Constraint neighborsChanneling(UndirectedGraphVar g, SetVar[] neighbors) {
return new Constraint("neighSetsChanneling",
new PropNeighSetsChannel1(neighbors, g), new PropNeighSetsChannel2(neighbors, g));
}
/**
* Channeling constraint:
* neighbors[i][j] = 1 <=> edge (i,j) in g
*
* @param g
* @param neighbors
*/
default Constraint neighborsChanneling(UndirectedGraphVar g, BoolVar[][] neighbors) {
return new Constraint("neighBoolsChanneling",
new PropNeighBoolsChannel1(neighbors, g), new PropNeighBoolsChannel2(neighbors, g));
}
/**
* Channeling constraint:
* int j in neighborsOf <=> edge (node,j) in g
*
* @param g
* @param neighborsOf
* @param node
*/
default Constraint neighborsChanneling(UndirectedGraphVar g, SetVar neighborsOf, int node) {
return new Constraint("neighSetChanneling",
new PropNeighSetChannel(neighborsOf, node, g, new IncidentSet.SuccessorsSet()));
}
/**
* Channeling constraint:
* neighborsOf[j] = 1 <=> edge (node,j) in g
*
* @param g
* @param neighborsOf
* @param node
*/
default Constraint neighborsChanneling(UndirectedGraphVar g, BoolVar[] neighborsOf, int node) {
return new Constraint("neighBoolChanneling",
new PropNeighBoolChannel(neighborsOf, node, g, new IncidentSet.SuccessorsSet()));
}
// Successors
/**
* Channeling constraint:
* int j in successors[i] <=> edge (i,j) in g
*
* @param g
* @param successors
*/
default Constraint successorsChanneling(DirectedGraphVar g, SetVar[] successors) {
return new Constraint("succSetsChanneling",
new PropNeighSetsChannel1(successors, g), new PropNeighSetsChannel2(successors, g));
}
/**
* Channeling constraint:
* successors[i][j] <=> edge (i,j) in g
*
* @param g
* @param successors
*/
default Constraint successorsChanneling(DirectedGraphVar g, BoolVar[][] successors) {
return new Constraint("succBoolsChanneling",
new PropNeighBoolsChannel1(successors, g), new PropNeighBoolsChannel2(successors, g));
}
/**
* Channeling constraint:
* int j in successorsOf <=> edge (node,j) in g
*
* @param g
* @param successorsOf
* @param node
*/
default Constraint successorsChanneling(DirectedGraphVar g, SetVar successorsOf, int node) {
return new Constraint("succSetChanneling",
new PropNeighSetChannel(successorsOf, node, g, new IncidentSet.SuccessorsSet()));
}
/**
* Channeling constraint:
* successorsOf[j] = 1 <=> edge (node,j) in g
*
* @param g
* @param successorsOf
* @param node
*/
default Constraint successorsChanneling(DirectedGraphVar g, BoolVar[] successorsOf, int node) {
return new Constraint("succBoolChanneling",
new PropNeighBoolChannel(successorsOf, node, g, new IncidentSet.SuccessorsSet()));
}
// Predecessors
/**
* Channeling constraint:
* int j in predecessorsOf <=> edge (j,node) in g
*
* @param g
* @param predecessorsOf
* @param node
*/
default Constraint predecessorsChanneling(DirectedGraphVar g, SetVar predecessorsOf, int node) {
return new Constraint("predSetChanneling",
new PropNeighSetChannel(predecessorsOf, node, g, new IncidentSet.PredecessorsSet()));
}
/**
* Channeling constraint:
* predecessorsOf[j] = 1 <=> edge (j,node) in g
*
* @param g
* @param predecessorsOf
* @param node
*/
default Constraint predecessorsChanneling(DirectedGraphVar g, BoolVar[] predecessorsOf, int node) {
return new Constraint("predBoolChanneling",
new PropNeighBoolChannel(predecessorsOf, node, g, new IncidentSet.PredecessorsSet()));
}
//***********************************************************************************
// DEGREE CONSTRAINTS
//***********************************************************************************
// degrees
/**
* Minimum degree constraint
* for any vertex i in g, |(i,j)| >= minDegree
* This constraint only holds on vertices that are mandatory
*
* @param g undirected graph var
* @param minDegree integer minimum degree of every node
* @return a minimum degree constraint
*/
default Constraint minDegree(UndirectedGraphVar g, int minDegree) {
return new Constraint("minDegree", new PropNodeDegreeAtLeastIncr(g, minDegree));
}
/**
* Minimum degree constraint
* for any vertex i in g, |(i,j)| >= minDegree[i]
* This constraint only holds on vertices that are mandatory
*
* @param g undirected graph var
* @param minDegrees integer array giving the minimum degree of each node
* @return a minimum degree constraint
*/
default Constraint minDegrees(UndirectedGraphVar g, int[] minDegrees) {
return new Constraint("minDegrees", new PropNodeDegreeAtLeastIncr(g, minDegrees));
}
/**
* Maximum degree constraint
* for any vertex i in g, |(i,j)| <= maxDegree
* This constraint only holds on vertices that are mandatory
*
* @param g undirected graph var
* @param maxDegree integer maximum degree
* @return a maximum degree constraint
*/
default Constraint maxDegree(UndirectedGraphVar g, int maxDegree) {
return new Constraint("maxDegree", new PropNodeDegreeAtMostIncr(g, maxDegree));
}
/**
* Maximum degree constraint
* for any vertex i in g, |(i,j)| <= maxDegrees[i]
* This constraint only holds on vertices that are mandatory
*
* @param g undirected graph var
* @param maxDegrees integer array giving the maximum degree of each node
* @return a maximum degree constraint
*/
default Constraint maxDegrees(UndirectedGraphVar g, int[] maxDegrees) {
return new Constraint("maxDegrees", new PropNodeDegreeAtMostIncr(g, maxDegrees));
}
/**
* Degrees constraint
* for any vertex i in g, |(i,j)| = degrees[i]
* A vertex which has been removed has a degree equal to 0
* ENSURES EVERY VERTEX i FOR WHICH DEGREE[i]>0 IS MANDATORY
*
* @param g undirected graph var
* @param degrees integer array giving the degree of each node
* @return a degree constraint
*/
default Constraint degrees(UndirectedGraphVar g, IntVar[] degrees) {
return new Constraint("degrees", new PropNodeDegreeVar(g, degrees));
}
// inDegrees
/**
* Minimum inner degree constraint
* for any vertex i in g, |(j,i)| >= minDegree
* This constraint only holds on vertices that are mandatory
*
* @param g directed graph var
* @param minDegree integer minimum degree of every node
* @return a minimum inner degree constraint
*/
default Constraint minInDegree(DirectedGraphVar g, int minDegree) {
return new Constraint("minInDegree", new PropNodeDegreeAtLeastIncr(g, Orientation.PREDECESSORS, minDegree));
}
/**
* Minimum inner degree constraint
* for any vertex i in g, |(j,i)| >= minDegree[i]
* This constraint only holds on vertices that are mandatory
*
* @param g directed graph var
* @param minDegrees integer array giving the minimum degree of each node
* @return a minimum inner degree constraint
*/
default Constraint minInDegrees(DirectedGraphVar g, int[] minDegrees) {
return new Constraint("minInDegrees", new PropNodeDegreeAtLeastIncr(g, Orientation.PREDECESSORS, minDegrees));
}
/**
* Maximum inner degree constraint
* for any vertex i in g, |(j,i)| <= maxDegree
* This constraint only holds on vertices that are mandatory
*
* @param g directed graph var
* @param maxDegree integer maximum degree
* @return a maximum inner degree constraint
*/
default Constraint maxInDegree(DirectedGraphVar g, int maxDegree) {
return new Constraint("maxInDegree", new PropNodeDegreeAtMostIncr(g, Orientation.PREDECESSORS, maxDegree));
}
/**
* Maximum inner degree constraint
* for any vertex i in g, |(j,i)| <= maxDegrees[i]
* This constraint only holds on vertices that are mandatory
*
* @param g directed graph var
* @param maxDegrees integer array giving the maximum degree of each node
* @return a maximum inner degree constraint
*/
default Constraint maxInDegrees(DirectedGraphVar g, int[] maxDegrees) {
return new Constraint("maxInDegrees", new PropNodeDegreeAtMostIncr(g, Orientation.PREDECESSORS, maxDegrees));
}
/**
* Degree inner constraint
* for any vertex i in g, |(j,i)| = degrees[i]
* A vertex which has been removed has a degree equal to 0
* ENSURES EVERY VERTEX i FOR WHICH DEGREE[i]>0 IS MANDATORY
*
* @param g directed graph var
* @param degrees integer array giving the degree of each node
* @return a degree inner constraint
*/
default Constraint inDegrees(DirectedGraphVar g, IntVar[] degrees) {
return new Constraint("inDegrees", new PropNodeDegreeVar(g, Orientation.PREDECESSORS, degrees));
}
// out-degrees
/**
* Minimum outer degree constraint
* for any vertex i in g, |(i,j)| >= minDegree
* This constraint only holds on vertices that are mandatory
*
* @param g directed graph var
* @param minDegree integer minimum degree of every node
* @return a minimum outer degree constraint
*/
default Constraint minOutDegree(DirectedGraphVar g, int minDegree) {
return new Constraint("minOutDegrees", new PropNodeDegreeAtLeastIncr(g, Orientation.SUCCESSORS, minDegree));
}
/**
* Minimum outer degree constraint
* for any vertex i in g, |(i,j)| >= minDegree[i]
* This constraint only holds on vertices that are mandatory
*
* @param g directed graph var
* @param minDegrees integer array giving the minimum degree of each node
* @return a minimum outer degree constraint
*/
default Constraint minOutDegrees(DirectedGraphVar g, int[] minDegrees) {
return new Constraint("minOutDegrees", new PropNodeDegreeAtLeastIncr(g, Orientation.SUCCESSORS, minDegrees));
}
/**
* Maximum outer degree constraint
* for any vertex i in g, |(i,j)| <= maxDegree
* This constraint only holds on vertices that are mandatory
*
* @param g directed graph var
* @param maxDegree integer maximum degree
* @return a maximum outer degree constraint
*/
default Constraint maxOutDegree(DirectedGraphVar g, int maxDegree) {
return new Constraint("maxOutDegrees", new PropNodeDegreeAtMostIncr(g, Orientation.SUCCESSORS, maxDegree));
}
/**
* Maximum outer degree constraint
* for any vertex i in g, |(i,j)| <= maxDegrees[i]
* This constraint only holds on vertices that are mandatory
*
* @param g directed graph var
* @param maxDegrees integer array giving the maximum outer degree of each node
* @return a outer maximum degree constraint
*/
default Constraint maxOutDegrees(DirectedGraphVar g, int[] maxDegrees) {
return new Constraint("maxOutDegrees", new PropNodeDegreeAtMostIncr(g, Orientation.SUCCESSORS, maxDegrees));
}
/**
* Outer degree constraint
* for any vertex i in g, |(i,j)| = degrees[i]
* A vertex which has been removed has a degree equal to 0
* ENSURES EVERY VERTEX i FOR WHICH DEGREE[i]>0 IS MANDATORY
*
* @param g directed graph var
* @param degrees integer array giving the degree of each node
* @return an outer degree constraint
*/
default Constraint outDegrees(DirectedGraphVar g, IntVar[] degrees) {
return new Constraint("outDegrees", new PropNodeDegreeVar(g, Orientation.SUCCESSORS, degrees));
}
//***********************************************************************************
// CYCLE CONSTRAINTS
//***********************************************************************************
/**
* g must form a cycle
* Empty graph is accepted
* @param g an undirected graph variable
* @return a cycle constraint
*/
default Constraint cycle(UndirectedGraphVar g) {
int m = 0;
int n = g.getNbMaxNodes();
for (int i = 0; i < n; i++) {
m += g.getPotentialNeighborsOf(i).size();
}
m /= 2;
Propagator pMaxDeg = new PropNodeDegreeAtMostIncr(g, 2);
if (g.getMandatoryNodes().size() <= 1) {
// Graphs with one node and a loop must be accepted
IntVar nbNodes = g.getModel().intVar(g.getMandatoryNodes().size(), g.getPotentialNodes().size());
g.getModel().ifThenElse(
g.getModel().intGeView(nbNodes, 2),
new Constraint("minDeg >= 2", new PropNodeDegreeAtLeastIncr(g, 2)),
new Constraint("minDeg >= 1", new PropNodeDegreeAtLeastIncr(g, 1))
);
return new Constraint("cycle",
new PropNbNodes(g, nbNodes),
pMaxDeg,
new PropConnected(g),
new PropCycle(g)
);
}
return new Constraint("cycle",
new PropNodeDegreeAtLeastIncr(g, 2),
pMaxDeg,
new PropConnected(g),
new PropCycle(g)
);
}
/**
* Cycle elimination constraint
* Prevent the graph from containing cycles
* e.g. an edge set of the form {(i1,i2),(i2,i3),(i3,i1)}
*
* @param g a graph variable
* @return A cycle elimination constraint
*/
default Constraint noCycle(UndirectedGraphVar g) {
return new Constraint("noCycle", new PropAcyclic(g));
}
/**
* Cycle elimination constraint
* Prevent the graph from containing circuits
* e.g. an edge set of the form {(i1,i2),(i2,i3),(i3,i1)}
*
* @param g a graph variable
* @return A cycle elimination constraint
*/
default Constraint noCircuit(DirectedGraphVar g) {
return new Constraint("noCycle", new PropAcyclic(g));
}
//***********************************************************************************
// CONNECTIVITY CONSTRAINTS
//***********************************************************************************
/**
* Creates a connectedness constraint which ensures that g is connected
*
* BEWARE : empty graphs or graph with 1 node are allowed (they are not disconnected...)
* if one wants a graph with >= 2 nodes he should use the node number constraint (nbNodes)
* connected only focuses on the graph structure to prevent two nodes not to be connected
* if there is 0 or only 1 node, the constraint is therefore not violated
*
* The purpose of CP is to compose existing constraints, and nbNodes already exists
*
* @param g an undirected graph variable
* @return A connectedness constraint which ensures that g is connected
*/
default Constraint connected(UndirectedGraphVar g) {
return new Constraint("connected", new PropConnected(g));
}
/**
* Creates a connectedness constraint which ensures that g is biconnected
* Beware : should be used in addition to connected
* The empty graph is not considered biconnected.
*
* @param g an undirected graph variable
* @return A connectedness constraint which ensures that g is biconnected
*/
default Constraint biconnected(UndirectedGraphVar g) {
return new Constraint("connected", new PropBiconnected(g));
}
/**
* Creates a connectedness constraint which ensures that g has nb connected components
*
* @param g an undirected graph variable
* @param nb an integer variable indicating the expected number of connected components in g
* @return A connectedness constraint which ensures that g has nb connected components
*/
default Constraint nbConnectedComponents(UndirectedGraphVar g, IntVar nb) {
return new Constraint("NbCC", new PropNbCC(g, nb));
}
/**
* Creates a constraint which ensures that every connected component of g has a number of nodes bounded by
* sizeMinCC and sizeMaxCC.
*
* @param g an undirected graph variable.
* @param sizeMinCC An IntVar to be equal to the smallest connected component of g.
* @param sizeMaxCC An IntVar to be equal to the largest connected component of g.
* @return A SizeCC constraint.
*/
default Constraint sizeConnectedComponents(UndirectedGraphVar g, IntVar sizeMinCC, IntVar sizeMaxCC) {
return new Constraint("SizeCC",
new PropGreaterOrEqualX_Y(new IntVar[]{sizeMaxCC, sizeMinCC}),
new PropSizeMinCC(g, sizeMinCC),
new PropSizeMaxCC(g, sizeMaxCC));
}
/**
* Creates a constraint which ensures that every connected component of g has a minimum number of
* nodes equal to sizeMinCC.
*
* @param g an undirected graph variable.
* @param sizeMinCC An IntVar to be equal to the smallest connected component of g.
* @return A SizeMinCC constraint.
*/
default Constraint sizeMinConnectedComponents(UndirectedGraphVar g, IntVar sizeMinCC) {
return new Constraint("SizeMinCC", new PropSizeMinCC(g, sizeMinCC));
}
/**
* Creates a constraint which ensures that every connected component of g has a maximum number of
* nodes equal to sizeMaxCC.
*
* @param g an undirected graph variable
* @param sizeMaxCC An IntVar to be equal to the largest connected component of g.
* @return A SizeMaxCC constraint.
*/
default Constraint sizeMaxConnectedComponents(UndirectedGraphVar g, IntVar sizeMaxCC) {
return new Constraint("SizeMaxCC", new PropSizeMaxCC(g, sizeMaxCC));
}
/**
* Creates a strong connectedness constraint which ensures that g has exactly one strongly connected component
*
* @param g a directed graph variable
* @return A strong connectedness constraint which ensures that g is strongly connected
*/
default Constraint stronglyConnected(DirectedGraphVar g) {
return nbStronglyConnectedComponents(g, g.getModel().intVar(1));
}
/**
* Creates a strong connectedness constraint which ensures that g has nb strongly connected components
*
* @param g a directed graph variable
* @param nb an integer variable indicating the expected number of connected components in g
* @return A strong connectedness constraint which ensures that g has nb strongly connected components
*/
default Constraint nbStronglyConnectedComponents(DirectedGraphVar g, IntVar nb) {
return new Constraint("NbSCC", new PropNbSCC(g, nb));
}
//***********************************************************************************
// TREE CONSTRAINTS
//***********************************************************************************
/**
* Creates a tree constraint : g is connected and has no cycle
*
* @param g an undirected graph variable
* @return a tree constraint
*/
default Constraint tree(UndirectedGraphVar g) {
return new Constraint("tree", new PropAcyclic(g), new PropConnected(g));
}
/**
* Creates a forest constraint : g has no cycle but may have several connected components
*
* @param g an undirected graph variable
* @return a forest constraint
*/
default Constraint forest(UndirectedGraphVar g) {
return new Constraint("forest", new PropAcyclic(g));
}
/**
* Creates a directed tree constraint :
* g forms an arborescence rooted in vertex 'root'
* i.e. g has no circuit and a path exists from the root to every node
*
* @param g a directed graph variable
* @param root the (fixed) root of the tree
* @return a directed tree constraint
*/
default Constraint directedTree(DirectedGraphVar g, int root) {
int n = g.getNbMaxNodes();
int[] nbPreds = new int[n];
for (int i = 0; i < n; i++) {
nbPreds[i] = 1;
}
nbPreds[root] = 0;
return new Constraint("directedTree"
, new PropArborescence(g, root)
, new PropNodeDegreeAtMostIncr(g, Orientation.PREDECESSORS, nbPreds)
, new PropNodeDegreeAtLeastIncr(g, Orientation.PREDECESSORS, nbPreds)
);
}
/**
* Creates a directed forest constraint :
* g form is composed of several disjoint (potentially singleton) arborescences
*
* @param g a directed graph variable
* @return a directed forest constraint
*/
default Constraint directedForest(DirectedGraphVar g) {
return new Constraint("directedForest",
new PropArborescences(g),
new PropNodeDegreeAtMostIncr(g, Orientation.PREDECESSORS, 1)
);
}
//***********************************************************************************
// PATH and REACHABILITY
//***********************************************************************************
// reachability
/**
* Creates a constraint which ensures that every vertex in g is reachable by a simple path from the root.
*
* @param g a directed graph variable
* @param root a vertex reaching every node
* @return A constraint which ensures that every vertex in g is reachable by a simple path from the root
*/
default Constraint reachability(DirectedGraphVar g, int root) {
return new Constraint("reachability_from_" + root, new PropReachability(g, root));
}
//***********************************************************************************
// CLIQUES
//***********************************************************************************
/**
* partition a graph variable into nb cliques
*
* @param g a graph variable
* @param nb expected number of cliques in g
* @return a constraint which partitions g into nb cliques
*/
default Constraint nbCliques(UndirectedGraphVar g, IntVar nb) {
return new Constraint("NbCliques",
new PropTransitivity(g),
new PropNbCC(g, nb),
new PropNbCliques(g, nb) // redundant propagator
);
}
//***********************************************************************************
// DIAMETER
//***********************************************************************************
/**
* Creates a constraint which states that d is the diameter of g
* i.e. d is the length (number of edges) of the largest shortest path among any pair of nodes
* This constraint implies that g is connected
*
* @param g an undirected graph variable
* @param d an integer variable
* @return a constraint which states that d is the diameter of g
*/
default Constraint diameter(UndirectedGraphVar g, IntVar d) {
return new Constraint("diameter",
new PropConnected(g),
new PropDiameter(g, d)
);
}
/**
* Creates a constraint which states that d is the diameter of g
* i.e. d is the length (number of edges) of the largest shortest path among any pair of nodes
* This constraint implies that g is strongly connected
*
* @param g a directed graph variable
* @param d an integer variable
* @return a constraint which states that d is the diameter of g
*/
default Constraint diameter(DirectedGraphVar g, IntVar d) {
return new Constraint("NbCliques",
new PropNbSCC(g, g.getModel().intVar(1)),
new PropDiameter(g, d)
);
}
//***********************************************************************************
// OPTIMIZATION CONSTRAINTS
//***********************************************************************************
/**
* Constraint modeling the Traveling Salesman Problem
*
* @param graphVar graph variable representing a Hamiltonian cycle
* @param costVar variable representing the cost of the cycle
* @param edgeCosts cost matrix (should be symmetric)
* @param lagrMode use the Lagrangian relaxation of the tsp
* described by Held and Karp
* {0:no Lagrangian relaxation,
* 1:Lagrangian relaxation (since root node),
* 2:Lagrangian relaxation but wait a first solution before running it}
* @return a tsp constraint
*/
default Constraint tsp(UndirectedGraphVar graphVar, IntVar costVar, int[][] edgeCosts, int lagrMode) {
Propagator[] props = ArrayUtils.append(cycle(graphVar).getPropagators(),
new Propagator[]{new PropCycleCostSimple(graphVar, costVar, edgeCosts)});
if (lagrMode > 0) {
PropLagrOneTree hk = new PropLagrOneTree(graphVar, costVar, edgeCosts);
hk.waitFirstSolution(lagrMode == 2);
props = ArrayUtils.append(props, new Propagator[]{hk});
}
return new Constraint("TSP", props);
}
/**
* Creates a degree-constrained minimum spanning tree constraint :
* GRAPH is a spanning tree of cost COSTVAR and each vertex degree is constrained
*
* BEWARE : assumes the channeling between GRAPH and DEGREES is already done
*
* @param graphVar an undirected graph variable
* @param degrees the degree of every vertex
* @param costVar variable representing the cost of the mst
* @param edgeCosts cost matrix (should be symmetric)
* @param lagrMode use the Lagrangian relaxation of the dcmst
* {0:no Lagrangian relaxation,
* 1:Lagrangian relaxation (since root node),
* 2:Lagrangian relaxation but wait a first solution before running it}
* @return a degree-constrained minimum spanning tree constraint
*/
default Constraint dcmst(UndirectedGraphVar graphVar, IntVar[] degrees,
IntVar costVar, int[][] edgeCosts,
int lagrMode) {
Constraint treeCstr = tree(graphVar);
treeCstr.ignore();
Propagator[] props = ArrayUtils.append(
treeCstr.getPropagators()
, new Propagator[]{
new PropTreeCostSimple(graphVar, costVar, edgeCosts)
, new PropMaxDegVarTree(graphVar, degrees)
}
);
if (lagrMode > 0) {
PropGenericLagrDCMST hk = new PropGenericLagrDCMST(graphVar, costVar, degrees, edgeCosts, lagrMode == 2);
props = ArrayUtils.append(props, new Propagator[]{hk});
}
return new Constraint("dcmst", props);
}
//***********************************************************************************
// SYMMETRY BREAKING CONSTRAINTS
//***********************************************************************************
/**
* Post a symmetry breaking constraint. This constraint is a symmetry breaking for
* class of directed graphs which contain a directed tree with root in node 0.
* (All nodes must be reachable from node 0)
* Note, that this method post this constraint directly, so it cannot be reified.
*
* This symmetry breaking method based on paper:
* Ulyantsev V., Zakirzyanov I., Shalyto A.
* BFS-Based Symmetry Breaking Predicates for DFA Identification
* //Language and Automata Theory and Applications. – Springer International Publishing, 2015. – С. 611-622.
*
* @param graph graph to be constrainted
*/
default void postSymmetryBreaking(DirectedGraphVar graph) {
Model m = ref();
// ---------------------- variables ------------------------
int n = graph.getNbMaxNodes();
// t[i, j]
BoolVar[] t = m.boolVarArray("T[]", n * n);
// p[i]
IntVar[] p = new IntVar[n];
p[0] = m.intVar("P[0]", 0);
for (int i = 1; i < n; i++) {
p[i] = m.intVar("P[" + i + "]", 0, i - 1);
}
// ---------------------- constraints -----------------------
// t[i, j] <-> G
new Constraint("AdjacencyMatrix", new PropIncrementalAdjacencyMatrix(graph, t)).post();
// (p[j] == i) ⇔ t[i, j] and AND(!t[k, j], 0 ≤ k < j)
for (int i = 0; i < n - 1; i++) {
IntVar I = m.intVar(i);
for (int j = 1; j < n; j++) {
BoolVar[] clause = new BoolVar[i + 1];
clause[i] = t[i + j * n];
for (int k = 0; k < i; k++) {
clause[k] = t[k + j * n].not();
}
Constraint c = m.and(clause);
Constraint pij = m.arithm(p[j], "=", I);
m.ifThen(pij, c);
m.ifThen(c, pij);
}
}
// p[i] ≤ p[i + 1]
for (int i = 1; i < n - 1; i++) {
m.arithm(p[i], "<=", p[i + 1]).post();
}
}
/**
* Post a symmetry breaking constraint. This constraint is a symmetry breaking for
* class of undirected connected graphs.
* Note, that this method post this constraint directly, so it cannot be reified.
*
* This symmetry breaking method based on paper:
* Ulyantsev V., Zakirzyanov I., Shalyto A.
* BFS-Based Symmetry Breaking Predicates for DFA Identification
* //Language and Automata Theory and Applications. – Springer International Publishing, 2015. – С. 611-622.
*
* @param graph graph to be constrainted
*/
default void postSymmetryBreaking(UndirectedGraphVar graph) {
Model m = ref();
// ---------------------- variables ------------------------
int n = graph.getNbMaxNodes();
// t[i, j]
BoolVar[] t = m.boolVarArray("T[]", n * n);
// p[i]
IntVar[] p = new IntVar[n];
p[0] = m.intVar("P[0]", 0);
for (int i = 1; i < n; i++) {
p[i] = m.intVar("P[" + i + "]", 0, i - 1);
}
// ---------------------- constraints -----------------------
// t[i, j] <-> G
new Constraint("AdjacencyMatrix", new PropIncrementalAdjacencyUndirectedMatrix(graph, t)).post();
// (p[j] == i) ⇔ t[i, j] and AND(!t[k, j], 0 ≤ k < j)
for (int i = 0; i < n - 1; i++) {
IntVar I = m.intVar(i);
for (int j = 1; j < n; j++) {
BoolVar[] clause = new BoolVar[i + 1];
clause[i] = t[i + j * n];
for (int k = 0; k < i; k++) {
clause[k] = t[k + j * n].not();
}
Constraint c = m.and(clause);
Constraint pij = m.arithm(p[j], "=", I);
m.ifThen(pij, c);
m.ifThen(c, pij);
}
}
// p[i] ≤ p[i + 1]
for (int i = 1; i < n - 1; i++) {
m.arithm(p[i], "<=", p[i + 1]).post();
}
}
/**
* Creates a symmetry breaking constraint. This constraint is a symmetry breaking for
* class of undirected connected graphs.
*
* This symmetry breaking method based on paper:
* Codish M. et al.
* Breaking Symmetries in Graph Representation
* //IJCAI. – 2013. – С. 3-9.
*
* @param graph graph to be constrainted
*/
default Constraint symmetryBreaking2(UndirectedGraphVar graph) {
int n = graph.getNbMaxNodes();
BoolVar[] t = ref().boolVarArray("T[]", n * n);
return new Constraint("symmBreak",
new PropIncrementalAdjacencyUndirectedMatrix(graph, t),
new PropSymmetryBreaking(t)
);
}
/**
* Creates a symmetry breaking constraint. This constraint is a symmetry breaking for
* class of undirected connected graphs.
*
* This symmetry breaking method based on paper:
* Codish M. et al.
* Breaking Symmetries in Graph Representation
* //IJCAI. – 2013. – С. 3-9.
*
* @param graph graph to be constrainted
*/
default Constraint symmetryBreaking3(UndirectedGraphVar graph) {
int n = graph.getNbMaxNodes();
BoolVar[] t = ref().boolVarArray("T[]", n * n);
return new Constraint("symmBreakEx",
new PropIncrementalAdjacencyUndirectedMatrix(graph, t),
new PropSymmetryBreakingEx(t)
);
}
}